a) 

$x_{AB} = x_B - x_A = 5 - (-2) = 7$

b) 

$x_I = \frac{x_A + x_B}{2} = \frac{-2 + 5}{2} = \frac{3}{2} = 1.5$

c) 

$2(x_A - x_M) + 5(x_B - x_M) = 0$

$2(-2 - x_M) + 5(5 - x_M) = 0$

$-4 - 2x_M + 25 - 5x_M = 0$

$21 - 7x_M = 0$

$7x_M = 21$

$x_M = 3$

d) 

$2(x_A - x_N) + 3(x_B - x_N) = -1$

$2(-2 - x_N) + 3(5 - x_N) = -1$

$-4 - 2x_N + 15 - 3x_N = -1$

$11 - 5x_N = -1$

$5x_N = 12$

$x_N = \frac{12}{5} = 2.4$